Examining the Effects of Sight Distance, Road Conditions, and Weather on Intersection Crash Severity: A Random Parameters Logit Approach with Heterogeneity in Means and Variances

Abstract

Intersections represent critical crash locations on road networks necessitating targeted safety interventions. This study employs a random parameters ordered logit (RPOL) model with heterogeneity in means to analyze injury severity contributing factors across 9108 Wyoming intersection crashes that occurred from 2007 to 2017. The analysis reveals that crashes on principal and minor arterial intersections are consistently associated with higher risks of severe/fatal injuries, while urban intersections exhibit less severe consequences, likely due to lower speeds and enhanced infrastructure. Adverse weather conditions, particularly snowy and icy road surfaces, increase the likelihood of property-damage-only (PDO) outcomes while reducing severe/fatal injuries. Temporal trends show a decline in crash severity over time, coinciding with advances in vehicle safety and policy improvements. Key behavioral factors, including left turn maneuvers and driver’s age heterogeneity, influence crash outcomes, whereas intersection sight distance (ISD) had no significant effect on crash severity underscoring data limitations requiring advanced analysis methods. This study’s findings prioritize the reconsideration of arterial intersection design, urban safety enhancements, and behavior-focused countermeasures for intersection safety.

1. Introduction

Intersections are among the most critical locations on the road network. They represent a significant proportion of traffic crashes, injuries, and fatalities. Each year, roughly a quarter of traffic fatalities and about half of all traffic injuries in the US are attributed to intersections. More than 50 percent of the combined total of fatal and injury crashes occur at or near intersections [1,2]. The complex interactions between vehicles, pedestrians, and other road users at intersections, compounded by varying road and environmental conditions, create a challenging environment for ensuring safety. Intersection safety is further complicated by increasing traffic volumes, evolving vehicle technologies, and the integration of multimodal operations. Consequently, improving intersection safety is one of the main priorities of the Federal Highway Administration (FHWA) and state Departments of Transportation (DOT), as evidenced by ongoing efforts to reduce crash severity and prevent fatalities [3].

The severity of crashes at intersections is influenced by a multitude of factors, including road geometry, environmental conditions, driver’s behavior, and the interaction of these elements. Among these, sight distance, road characteristics, and weather conditions are particularly critical in determining crash outcomes [4]. Sight distance limitations at curves or those that result from sight obstructions near intersections impede a driver’s ability to perceive and react to roadway hazards [5,6]. Roadway characteristics, including surface type, lane configuration, and the presence of a median, significantly affect vehicle control and maneuverability, particularly during abrupt braking or swerving. Weather conditions, such as rain, snow, and ice, exacerbate these risks by reducing visibility and traction, factors which are crucial for safely navigating intersections [5,7,8].

In Wyoming, where this study is based, intersection safety is further challenged by the state’s unique climatic and geographic conditions. Wyoming experiences one of the highest snowfall rates in the US, with a substantial proportion of crashes occurring on snowy, icy, or slushy surfaces [9,10]. Nearly one-third of all crashes in the state occur on non-dry pavement surfaces, which highlights the significance of examining roadway and environmental factors. Additionally, sight distance issues are prevalent in Wyoming, where high-speed roads are characterized by intersections posing an elevated risk of severe crashes [11,12]. Insufficient intersection sight distance (ISD) compounds these risks since it is a source of uncertainty in drivers’ decisions taken when navigating intersections. The ISD refers to the distance a driver must observe at an intersection to make appropriate maneuvers. It provides a clear line of sight for drivers to detect approaching vehicles or pedestrians, allowing them to respond and navigate intersections safely [13,14,15].

While previous research has examined crash severity at intersections, many studies have relied on traditional models with fixed parameters, which fail to capture the inherent variability in driver behavior and environmental conditions [13,16,17]. Recent advances in crash modeling, such as the proposition of random parameter models with heterogeneity in means and variances, offer a more nuanced understanding of crash severity dynamics [6,18,19,20]. These models allow for the analysis of unobserved heterogeneity, capturing variations in how road and weather conditions affect crash severity across different intersection types and scenarios. For instance, studies have demonstrated that random parameter models can effectively account for unobserved heterogeneity in crash data leading to more accurate predictions of injury severity risks [21,22]. Additionally, incorporating heterogeneity in means and variances enables the models to capture the influences of varying conditions on crash outcomes more precisely.

A Random Parameters Ordered Logit (RPOL) model extends traditional regression approaches by allowing certain coefficients to vary randomly across observations, thereby accommodating the natural variability in crash-influencing factors. This flexibility enables the model to account for unobserved heterogeneity, differences in crash outcomes that arise from factors not explicitly included in the dataset, such as subtle variations in driver behavior or local road conditions [19]. Further, heterogeneity in means and variances refers to the model’s ability to let the central tendency and variability of these random parameters be influenced by observed variables (e.g., weather or road type) [20]. This added layer captures how the effects of certain factors can differ systematically across contexts, enhancing the model’s precision and interpretability. These concepts are essential to modern safety analytics, especially when analyzing complex crash phenomena at intersections.

To synthesize the evolution of methodologies and variables used in intersection crash severity research, Table 1 summarizes key studies that have informed the current modeling framework. These works span areas such as unobserved heterogeneity, sight distance limitations, geometric configurations, surface conditions, weather impacts, and driver behavior, all of which are critical to understanding injury severity dynamics in intersection-related crashes.

Table 1. Summary of key literature on intersection crash severity modeling.

Study	Domain	Methodology	Findings
[23,24,25]	Crash Data Modeling	Random Parameters Logit, Mixed Logit	Emphasized the significance of accounting for unobserved heterogeneity effects to enhance model accuracy and inference in crash severity studies
[26,27]	Simulation and Estimation Techniques in Random Parameter Models	Simulated Maximum Likelihood Estimation, Halton Draws	Outlined techniques for simulating likelihood functions in discrete choice models and improving estimation precision
[19,20,21,22]	Crash Severity Models Using Heterogeneity in Means and Variances	Random Parameters Logit with Heterogeneity in Means and Variances	Demonstrated how modeling heterogeneity effects improves behavioral aspects’ interpretation and model performance across demographic and environmental contexts
[13,14,16]	Geometric Sight Constraints at Intersections	Empirical Safety Analysis	Examined how limited sight distance, curvature, and intersection geometry influence crash severity, especially at stop-controlled intersections and on curved segments
[5,7,8]	Roadway Design and Intersection Characteristics	Logistic Regression, Mixed-Effects Modeling	Linked crash severity with features such as medians, lanes, roadway surface types, and pavement conditions
[8,10,11]	Surface Condition and Geometric Risks in Mountainous Terrain	Mixed Logit, Empirical Analysis	Explored the role of friction, grade, and geometric alignment in crash incidence, especially in mountainous regions
[9,10]	Weather-Driven Behavioral Adaptation in Crashes	Statistical Time-Series, Logistic Models	Observed compensatory driving behavior under adverse weather (e.g., snow), resulting in reduced crash severity despite increased crash frequency
[6,7]	Intersection Geometry and Surface-Related Crash Outcomes	Regression-Based Safety Modeling	Identified intersection configuration and pavement type as key contributors to injury severity
[17,20]	Spatial and Area-Type Influences on Crash Severity	Ordered Probit, Cross-Sectional Analysis	Rural roads and intersections showed higher severity due to higher speeds and longer emergency response times

By employing advanced modeling techniques, this study addresses critical gaps in the literature by comprehensively analyzing the effects of sight distance, road characteristics, and weather conditions on crash severity at or near intersections. Specifically, a random parameters logit model with heterogeneity in means and variances is utilized to account for unobserved heterogeneity effects and the varying influences of explanatory variables across different crash scenarios. This approach provides a nuanced understanding of how intersection-related factors contribute to crash severity. This will assist in guiding policymakers and transportation agencies in developing targeted safety interventions and infrastructure improvements to mitigate crash severity at intersections.

This study adds to the growing body of RPOL-based crash research by addressing a broader and more complex setting: intersection crashes across the state of Wyoming. Prior studies using similar methods have focused on highly specific crash types—such as motorcycles, hybrid vehicles, pedestrian zones, or rear-end collisions in work zones—often with older and smaller datasets limited to certain states [19,20,21,22]. In contrast, we analyze a decade of comprehensive crash data involving various vehicle types, road users, and intersection configurations, under diverse environmental conditions. This study also incorporates underutilized variables like ISD and applies heterogeneity in both means and variances, yielding improved explanatory power and relevance for intersection safety policy.

2. Data Collection and Description

This study analyzed crash data obtained from the Critical Analysis Reporting Environment (CARE) system that is managed by the Wyoming Department of Transportation (WYDOT). These records were compiled from police crash reports and integrated into the environment. The dataset is structured so that each entry represents a unique crash record that occurred at or near an intersection. The analysis covered 9108 unique crash records from 359 intersections across Wyoming from January 2007 to December 2017, excluding 2010 and 2011 due to inconsistencies and incomplete reporting in key crash attributes during those years, and not available online in the CARE database. A summary of the descriptive statistics for the crash data is provided in Table 2. Intersection crashes are defined as those that occur within 250 feet (76.2 m) of the center of the intersection, as per some transportation agencies [14,28,29].

Table 2. Intersection Data’s Descriptive Statistics.

Crash Severity
Dependent Variable Outcome		Count	Percent
Property damage only (PDO) crash		6915	75.9
Serious injury crash		2032	22.3
Severe/Fatal injury crash		161	1.8
Variable	Descriptions	Yes	No	Percent Yes
Roadway Characteristics
Four-leg intersection	1 if intersection has four legs; 0 otherwise	7389	1719	81.1
Other than a four-legged intersection	1 if intersection is other than four legs; 0 otherwise	1719	7389	18.9
Urban area	1 if a crash occurred in an urban area; 0 otherwise	8530	578	93.7
Rural area	1 if a crash occurred in a rural area; 0 otherwise	578	8530	6.3
Interstate road	1 if a crash occurred on an interstate; 0 otherwise.	213	8895	2.4
Principal arterial road	1 if a crash occurred on a principal arterial; 0 otherwise.	8078	1030	88.7
Minor arterial road	1 if a crash occurred on an arterial; 0 otherwise.	563	8545	6.2
Collector road	1 if a crash occurred on a collector road; 0 otherwise.	190	8918	2.1
Two-Lane road	1 if a crash occurred on a road with 2 lanes; 0 otherwise.	1298	7810	14.2
Four-Lane road	1 if a crash occurred on a road with 4 lanes; 0 otherwise.	7810	1298	85.8
Asphalt surface	1 if a crash occurred on an asphalt road; 0 otherwise.	4153	4955	45.6
Concrete surface	1 if a crash occurred on a concrete road; 0 otherwise.	4623	4485	50.8
Level grade	1 if road grade is level; 0 otherwise	820	8288	9.0
Non-level grade	1 if road grade is up or down; 0 otherwise	8288	820	91.0
Raised median	1 if a raised median is present; 0 otherwise.	4918	4190	54.3
Pedestrian involved	1 if a pedestrian was involved in the crash; 0 otherwise.	101	9007	1.1
School bus involved	1 if a school bus was involved in the crash; 0 otherwise.	35	9073	0.4
ISD * obstructed	1 if the intersection sight distance was obstructed; 0 otherwise.	165	8943	1.8
Single-Vehicle crash	1 if the crash involved a single vehicle; 0 otherwise	975	8133	10.7
Multi-Vehicle crash	1 if the crash involved 2 or more vehicles; 0 otherwise	8133	975	89.3
Environmental Characteristics
Non-dry surface (wet, snowy, slushy, icy, frosty)	1 if the surface was wet, snowy, slushy, icy, or frosty; 0 otherwise.	2521	6587	27.7
Dry surface	1 if the surface was dry; 0 otherwise.	6544	2564	71.8
Clear weather	1 if the weather was clear; 0 otherwise	7316	1792	80.3
Snowing	1 if it was snowing at the time of the crash; 0 otherwise.	1031	8077	11.3
Raining	1 if it was raining at the time of the crash; 0 otherwise.	316	8792	3.4
Cloudy	1 if the weather was cloudy at the time of the crash; 0 otherwise.	346	8762	3.8
Darkness	1 if the light condition was darkness; 0 otherwise	1726	7382	19.0
Daylight	1 if light condition daylight; 0 otherwise	7025	2083	77.1
Dawn or dusk light	1 if the light condition was dawn or dusk	327	8781	3.6
Temporal Aspects
Weekdays	1 if a crash occurred on a weekday	7330	1778	80.5
Weekend **	1 if a crash occurred on a Saturday and Sunday	1778	7330	19.5
Spring	1 if a crash occurred in spring (March-May); 0 otherwise	1916	7192	21.0
Summer	1 if a crash occurred in summer (June-August); 0 otherwise.	2268	6840	24.9
Fall	1 if a crash occurred in fall (September-November); 0 otherwise.	2225	6883	24.4
Winter	1 if a crash occurred in winter (December-February); 0 otherwise.	2699	6409	29.6
Maneuver at Intersection
Variable		Yes	No	Percent Yes
Maneuvering straight	1 if the vehicle was moving straight; 0 otherwise	4590	4518	50.4
Turning left	1 if the vehicle was turning left; 0 otherwise	1732	7376	19.0
Turning right	1 if the vehicle was turning right; 0 otherwise.	739	8369	8.1
Passing	1 if the vehicle was passing; 0 otherwise.	392	8716	4.3
Signalized intersection	1 if the intersection was controlled by a traffic signal; 0 otherwise	5650	3458	62.0
Sign-controlled intersection	1 if the intersection was controlled by a stop or yield sign; 0 otherwise.	648	8460	7.1
Flashing yellow controlled intersection	1 if the intersection was controlled by a flashing yellow signal; 0 otherwise.	202	8906	2.2
Speeding	1 if the speed of the vehicle is more than the posted speed; 0 otherwise.	703	8405	7.7
Driver Characteristics
Male driver	1 if the driver was male; 0 otherwise	5156	3952	56.6
Female driver	1 if the driver was female; 0 otherwise	3634	5474	39.9
Driver’s Age Group (Years)		Count	Percent
≤20		1840	20.2%
20–30		2135	23.4%
30–40		1384	15.2%
40–50		1134	12.5%
50–60		1069	11.7%
>60		1546	16.9%
Continuous Variables
Variable		Mean	Minimum	Maximum
Number of Vehicles in the Crash	Count of vehicles involved (continuous).	1.96	1.00	7.00
Friction Number	Measure of pavement friction (continuous).	39.56	18.65	71.00
Estimated Speed (km/h)	Pre-crash estimated speed in km/h (continuous).	36.84	0	128.75
Driver Age	Age of the driver in years (continuous)	39.92	9	100

* ISD = Intersection sight distance; ** = Weekend is only Saturday and Sunday.

In addition to the crash data illustrated in Figure 1, a variety of roadway, environmental, and crash-specific relevant attributes data were collected. Intersection locations are identified and linked with their corresponding attributes to create a comprehensive dataset. This dataset serves as the foundation for analyzing the influence of sight distance, road characteristics, and weather conditions on crash severity outcomes.

Figure 1. Geographic Information System-based map of Wyoming’s intersection crashes.

Crash severity in this study is classified into three ordinal categories: PDO crashes, serious crashes that result in non-fatal but grave injuries (e.g., broken bones, internal injuries, or hospitalization), and severe/fatal crashes involving life-threatening injuries (e.g., traumatic brain injury, spinal cord damage) or fatalities. In the dataset, PDO crashes dominate (75.9%), followed by serious injury crashes (22.3%) and severe/fatal injury crashes (1.8%). To ensure a consistent and complete dataset for modeling, observations with missing data for any of the variables included in the final models were excluded from the analysis, following a listwise deletion approach; this resulted in the removal of less than 1% of the original records.

2.1. Roadway Characteristics

The dataset reveals that 81.1% of crashes occurred at four-leg intersections, with the remainder at other intersection types. Other intersections include T-intersections, Y-intersections, railroad crossings, and intersections belonging to interchanges. Urban area crashes represent the vast majority of the crashes in the data (93.7%), while rural area crashes account for 6.3% underscoring the prevalence of urban intersection safety concerns. Regarding roadway functional classifications, 88.7% of the crashes occur on principal arterials, followed by 6.2% on minor arterials, 2.4% on interstates, and 2.1% on collectors. Notably, 85.8% of the crashes are on two-lane roads, while four-lane roads share 14.2% of the crashes.

The statistics also highlight the significance of roadway surface and grade attributes in intersection safety. Asphalt surfaces are present in 45.6% of the crashes, while concrete surfaces are present in 50.8%. Crashes occurring on non-level grades account for 91.0% while the remaining 9.0% of the crashes are observed to occur on level surfaces. Raised medians, associated with improved traffic control, are present in 54.3% of the crashes, whereas pedestrian-related crashes are relatively rare, comprising only 1.1% of the crash records. Moreover, crashes involving school buses and intersections with obstructed ISD are minimal at 0.4% and 1.8%, respectively.

2.2. Environmental Characteristics

Adverse environmental conditions play a substantial role in crash occurrences. Non-dry surfaces, including wet, snowy, icy, slushy, and frosty roads, account for 27.7% of the crashes, while dry surfaces are observed in 71.8% of the crashes. Possibly, dry roads are favorable for travel, leading to higher exposure and, resultantly, more crashes. Clear weather conditions prevail in 80.3% of the crashes, with snowy, rainy, and cloudy weather contributing to 11.3%, 3.4%, and 3.8% of the crashes, respectively. Non-daylight conditions, such as darkness or twilight conditions, are associated with 19.0% of the crashes, while daylight conditions account for 77.1% of the crashes.

2.3. Temporal Variables

Temporal patterns indicate that crashes are more likely to occur on weekdays (80.5%) than on weekends (19.5%). Seasonal variations are evident with 29.6% of the crashes occurring in the winter, followed by 24.9% in the summer, 24.4% in the fall, and 21.0% in the spring. This distribution underscores the influence of weather and road conditions during the winter months on intersection safety.

2.4. Drivers’ Characteristics

Drivers’ behaviors and demographics also provide critical insights. Male drivers are involved in 56.6% of the crashes compared to 39.9% of the female drivers. Age distributions reveal a wide range, with drivers aged between 20 and 30 years accounting for the highest proportion (23.4%), followed by those aged 20 years and younger (20.2%) and those who are older than 60 (16.9%).

2.5. Maneuvers at Intersections

Drivers’ maneuvers at intersections provide additional context for crash dynamics. Maneuvering straight is the most common action involved in 50.4% of the crashes, followed by left turns (19.0%) and right turns (8.1%). Intersections controlled by traffic signals account for 62.0% of the crashes, while those controlled by traffic signs and flashing yellow signals contribute to 7.1% and 2.2% of the crashes, respectively. Speeding is also a contributing factor in 7.7% of the crashes.

2.6. Continuous Variables

Several continuous variables also provide critical insights. The number of vehicles involved in the crashes ranged from 1 to 7, with an average of 1.96 vehicles per crash. Speed-related characteristics further highlight intersection risks, considering that estimated speeds during the crashes range from 0 to 128.7 km/h (mean: 36.84 km/h). The average driver’s age is 39.9 years, with a range of 9 to 100 years.

3. Data Analysis Methodology

This study applies an RPOL model with heterogeneity in means and variances to examine the impact of the crash contributing factors on injury severity risks. The RPOL framework accounts for unobserved heterogeneity across observations, a critical aspect in modeling complex behaviors such as crash outcomes [21]. Unlike fixed-parameter models, the RPOL structure allows coefficient estimates to vary across observations, capturing more nuanced effects [24,27]. By incorporating heterogeneity in both means and variances, the model achieves greater flexibility and improves inference reliability [21,22,30].

To analyze crash severity outcomes (PDO, serious injury, severe/fatal crashes), the RPOL model is estimated using the Rchoice package in the data analysis software, R [31,32]. It is based upon a latent utility framework where the utility, U_ij, for crash i and severity outcome j is defined as follows:

$$U_{ij}={\mathbf{X}}_{ij}{\mathsf{\beta }}_i+{\epsilon }_{ij}$$

(1)

In Equation (1), ${\mathbf{X}}_{ij}$ is a vector of observed explanatory variables (e.g., roadway characteristics, environmental factors, and driver’s behavior, among others) for crash i and severity category j. The parameters vector β_i represents how each crash i’s severity is influenced by these explanatory variables, and the parameters vary randomly across observations. Unlike standard logit models, the coefficients follow a specified probability distribution rather than remaining fixed. In this context, ε_ij denotes the error term, which follows a logistic distribution, consistent with the ordinal logit specification. Given this specification, the probability, P_i(j), that crash i results in severity category j is given by the following expression:

$$P_i\left(j\right)=\underset{\mathsf{\beta }}{\int }{\displaystyle \frac{\exp \left({\mathbf{X}}_{ij}{\mathsf{\beta }}_i\right)}{{\sum }_{m=1}^J\exp \left({\mathbf{X}}_{im}{\mathsf{\beta }}_i\right)}}f(\mathsf{\beta }\mid \mathsf{\varphi })d\mathsf{\beta }$$

(2)

The term f(β∣ϕ) is the density function of the random parameters βs, and ϕ represents the vector of the parameters’ distributional properties, namely their means and variances [25]. The term J is the total number of severity outcomes, 3, which corresponds to PDO, serious injury, and severe/fatal injury crashes. This equation integrates over the distributions of the βs, explicitly accounting for unobserved heterogeneity effects across crashes. The likelihood function aggregates these probabilities across all crashes as follows:

$$L\left(\mathsf{\theta }\right)=\prod _{i=1}^N\int \left[\prod _{j=1}^{J}P(y_i=j\mid {\mathsf{\beta }}_i)\right]f\left({\mathsf{\beta }}_i∣\mathsf{\theta }\right)d{\mathsf{\beta }}_i$$

(3)

In Equation (3), N is the total number of crashes, P(y_i = j∣β_i) is the conditional probability of crash i resulting in severity category j, and f (β_i∣θ) is the density function of the random parameters, βs. Since the integral of Equation (3) is intractable analytically, simulation techniques such as the Halton draws are implemented for numerical approximation [27]. In the Rchoice package, random parameters are specified using the ranp argument.

The ordinal structure of the dependent variable is preserved using the threshold parameter κ_j that is estimated within the ordered logit framework of the Rchoice package. The probability of crash i resulting in severity category j is given by the following formula:

$$P\left(y_i=j\right)=\mathsf{\Lambda }\left({\kappa }_j-{\mathbf{X}}_i{\mathsf{\beta }}_i\right)-\mathsf{\Lambda }\left({\kappa }_{j-1}-{\mathbf{X}}_i{\mathsf{\beta }}_i\right)$$

(4)

The operator, Λ(⋅), is the logistic cumulative distribution function (CDF). Consistent with econometric standards for ordered outcomes [33,34], the thresholds satisfy the inequality, κ_j−1 < κ_j, to ensure monotonicity with κ₀ = −∞ and κ₃ = ∞ defining the latent utility boundaries. The crashes are classified as follows:

• PDO if U_i ≤ κ₁,
• Serious injury if κ₁ < U_i ≤ κ₂, and
• Severe/Fatal crash if U_i > κ₂

This specification accounts for both observed heterogeneity (via ${\mathbf{X}}_i{\mathsf{\beta }}_i$) and unobserved heterogeneity (through the random parameters in β) align with best practices in crash severity analysis [35].

To approximate the computationally intractable integral of the mixed logit probability structure, the model employs simulated maximum likelihood estimation (SMLE) with 800 Halton draws, a quasi-Monte Carlo method known for its computational efficiency [27]. This count of draws was found to be sufficient in prior studies for accurate parameter estimation [23,26]. The model is optimized via the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm, which is a quasi-Newton optimization method that is used for solving unconstrained nonlinear optimization problems.

The selection of explanatory variables is guided by theoretical foundations and supported by prior empirical studies on crash severity [30,36]. These include temporal variables (e.g., year, weekday), roadway characteristics (e.g., arterial roads, medians, intersection type), environmental conditions (e.g., snow, rain, darkness), and behavioral factors (e.g., speeding, turning maneuvers, pedestrian involvement).

For variables such as the driver’s age, speeding, and pedestrian involvement, random parameters are specified to capture unobserved heterogeneity in their effects. For instance, driver’s age variability is linked to risk-taking behavior among younger drivers and slower reaction times among older drivers [22,37]. Speeding effects may vary nonlinearly with roadway design and enforcement presence [38,39] while heterogeneity in pedestrian involvement reflects unmeasured factors, including visibility conditions and infrastructure differences [38]. Likelihood ratio tests confirmed model improvement consistent with methodological guidance on capturing unobserved heterogeneity through random parameters [23,24]. By integrating random parameters with heterogeneity in means and variances, this approach provides a comprehensive and robust framework for analyzing the determinants of crash injury severity.

It is important to note that this study focuses on the in-sample estimation of parameters to understand the relationship between contributing factors and crash severity. While the models demonstrate a good fit to the data used for estimation, their predictive performance on unseen data was not validated through a training-test split or cross-validation. Such predictive validation represents a valuable direction for future research. Furthermore, the distribution of crash severity outcomes in the dataset, with severe/fatal crashes being less frequent, is representative of real-world crash patterns and was accounted for within the model’s probabilistic framework.

4. Results and Analysis

This section presents the results and interpretations of the RPOL models that are estimated to examine the factors that influence intersection crash injury severity risks. The models include one for single-vehicle crashes, of which results are presented in Table 3, and one for crashes involving two or more vehicles, of which results are presented in Table 4. Model comparison statistics are summarized in Table 5. The 95th percentile confidence interval (CI) is used as the basis for retaining or otherwise excluding parameters from the models. Statistically significant parameters from the model’s results are shown only. To enhance interpretability, average marginal effects (AMEs) are calculated, highlighting the impact of each variable on the probability of PDO, serious injury, and severe/fatal injury outcomes. The discussion is organized by thematic categories of predictors, such as roadway characteristics, environmental conditions, and behavioral factors to provide deeper insight into their effects.

Table 3. Single-Vehicle Crashes Model.

Coefficients:	Estimate	Standard Deviation	Error	z-Value	AME: PDO	AME: Serious	AME: Severe/Fatal
κ1	3.116	0.189	16.456	<0.001	N/A	N/A	N/A
Constant	−0.124	0.254	−0.487	0.627	N/A	N/A	N/A
Non-Random Parameters
Season_winter (Reference: summer)	−0.428	0.179	−2.390	0.017	0.061	−0.045	−0.016
Area_urban (Reference: rural area)	0.432	0.209	2.063	0.039	−0.071	0.052	0.019
Light_darkness (Reference: daylight)	−0.361	0.152	−2.376	0.018	0.058	−0.042	−0.016
Road_wet_SnowSlushIceFrost (Reference: dry road surface)	−0.713	0.213	−3.354	0.001	0.131	−0.095	−0.036
Weather_snowing (Reference: clear weather)	−0.719	0.312	−2.308	0.021	0.128	−0.093	−0.035
DividedHighway (Reference: undivided highway)	−0.595	0.185	−3.221	0.001	0.113	−0.082	−0.031
Random Parameters
Pedestrian Involvement Mean	2.695	0.285	9.444	<0.001	−0.172	0.124	0.048
Pedestrian Involvement Standard Deviation	0.003	0.424	0.006	0.995	N/A	N/A	N/A
Driver 1’s Age Mean	−0.008	0.003	−2.362	0.018	0.003	−0.002	−0.001
Driver’s Age Standard Deviation	0.00002	0.004	0.005	0.996	N/A	N/A	N/A

Note: All parameters in the table are significant at a 95% confidence level. Column headings are bold and apply to all values in their columns.

Table 4. Multi-Vehicle Crashes Model.

Coefficients:	Estimate	Std.	Error	z-Value	AME: PDO	AME: Serious	AME: Severe/Fatal
κ1	3.095	0.095	32.696	<0.001	N/A	N/A	N/A
Constant	−0.545	0.159	−3.417	0.001	N/A	N/A	N/A
Non-Random Parameters
Year_13 (Reference: 2007)	−0.208	0.077	−2.710	0.007	0.036	−0.026	−0.010
Year_14 (Reference: 2007)	−0.172	0.077	−2.254	0.024	0.030	−0.022	−0.008
Year_16 (Reference: 2007)	−0.255	0.108	−2.368	0.018	0.049	−0.036	−0.013
Week_days (Reference: Weekend days)	−0.213	0.067	−3.186	0.001	0.041	−0.030	−0.011
Urban area (Reference: non-urban area)	−0.774	0.119	−6.484	<0.001	0.163	−0.116	−0.047
Road_collector (Reference: Interstate)	−0.650	0.258	−2.523	0.012	0.118	−0.085	−0.033
Narrow median (Reference: Wide median)	0.169	0.055	3.048	0.002	−0.041	0.029	0.012
Dry Road surface (Reference: Non-dry road surface)	0.185	0.074	2.493	0.013	−0.045	0.032	0.013
Snowing (Reference: clear weather)	−0.360	0.116	−3.101	0.002	0.061	−0.044	−0.017
Turning left (Reference: Moving straight)	0.319	0.064	4.954	<0.001	−0.064	0.045	0.019
Turning right (Reference: Moving straight)	−0.994	0.149	−6.690	<0.001	0.189	−0.133	−0.056
Traffic signal control (Reference: No control)	0.299	0.063	4.731	<0.001	−0.058	0.041	0.017
Sign control (Reference: No control)	0.260	0.115	2.273	0.023	−0.048	0.034	0.014
Random Parameter
Driver 1’s age Mean	−0.003	0.001	−2.588	0.010	0.002	−0.002	−0.001
Driver’s age Standard deviation	0.0004	0.009	0.043	0.966	NA	NA	NA

Note: All parameters in the table are significant at a 95% confidence level. Column headings are bold and apply to all values in their columns.

Table 5. Model Comparison.

Model	Single Vehicle Crashes Model		Multiple Vehicle Crashes Model
Heterogeneity	Yes	No	Yes	No
Number of Observations	975		8133
Number of Parameters	10	6	15	13
Log-Likelihood	−656	−671	−4620	−4995
AIC	1339	1333	9274	10,021
BIC	1396	1382	9408	10,143
Pseudo R2	0.111	0.093	0.075	0.065

4.1. Roadway Class and Region

The roadway functional classification and area type variables exhibited clear and meaningful effects on crash severity. Crashes on collector roads were associated with an 11.8% increase in PDO crashes, along with 8.5% and 3.3% reductions in serious and severe/fatal injuries, respectively (Table 4), highlighting the role of collector road design in lowering injury severity risk. These effects were statistically significant. These findings align with earlier studies that have attributed the occurrences of crashes on collectors to vehicle speeds, number of lanes, and traffic volumes [5,40].

The urban road intersection environment demonstrated a consistent trend across models. In the multi-vehicle crashes model (Table 4), urban crashes were linked to a 16.3% increase in PDO crashes, an 11.6% reduction in serious injury crashes, and a 4.7% decrease in severe/fatal injury crashes reflecting the pronounced difference in crash injury severity risks of urban intersections and rural intersections. These differences likely stem from factors such as lower driving speeds, denser signalization, pedestrian infrastructure, and faster emergency response times. These results reinforce previous findings [41,42,43] that observed lower injury severity risks at urban intersections. Features such as improved lighting, pedestrian infrastructure, and quicker emergency response, together with more cautious driving in congested settings, contribute to safer outcomes even in complex multi-vehicle crashes [5,41,42,43,44,45].

No statistically significant effects were found for geometric elements such as non-level grades or the number of lanes in the models. This may indicate that their influence is either limited or overshadowed by the stronger effects of functional class, area type, and behaviorally linked speed characteristics.

4.2. Environment and Surface Characteristics

Environmental and road surface conditions demonstrated significant impacts on intersection crash severity, supporting behavioral adaptation theory and existing empirical literature. Contrary to the assumption that adverse conditions necessarily increase injury severity, the analysis revealed that snow and dark lighting conditions were associated with lower injury severity outcomes and more PDO crashes, likely due to more cautious driving behaviors.

Snowy conditions were associated with decreased probabilities of severe/fatal and serious injuries and increased PDO crashes. In the Multi-Vehicle Model (Table 4), snowing increased PDO crash probability by 6.1%, while reducing serious injuries by 4.4% and severe/fatal outcomes by 1.7%. In single-vehicle crashes, the effect was stronger, with PDO probability increasing by 12.8% and serious and severe/fatal injuries decreasing by 9.3% and 3.5%, respectively. These protective effects support the behavioral adaptation hypothesis [9,46], which posits that drivers respond to perceptible hazards by reducing speed, increasing headways, and driving more cautiously, thereby lowering crash severity. Others reported that while snowfall may increase the overall frequency of crashes (especially nonfatal injury and PDO crashes), it might be associated with lower severity crashes compared to collisions in clear weather [9,47]. The likelihood of PDO crashes may increase due to the sliding and loss of control while maneuvering. There has been a negative relationship between snowfall and crash severity in some cases [48,49]. This was explained by risk compensation and reduced exposure in winter. Likewise, during adverse weather conditions, people tend to avoid unnecessary travel and show more focused and cautious driving behavior.

Road surface conditions similarly exhibited statistically significant effects. In the Single-Vehicle Model, road surfaces coded as “wet, icy, snowy, slushy, or frosted” were associated with an increased probability of PDO crashes by 13.1% and reduced serious and severe/fatal injuries by 9.5% and 3.6%, respectively. The protective nature of adverse surface conditions again supports the notion that drivers behave more conservatively under visible risk. These results align with [50], who found that on wet and snow/ice surfaces, the likelihood of serious injuries was lower than in crashes on dry surfaces.

In contrast, dry roads were associated with reductions in PDO crashes and increases in serious and severe/fatal injuries in the Multi-Vehicle Model (Table 4). Specifically, dry surfaces were linked to a 4.5% decrease in PDO crashes, along with 3.2% and 1.3% increases in serious and severe/fatal injuries, respectively. These results suggest that drivers may adopt riskier behaviors, such as higher speeds or reduced attention, on perceived safe surfaces, increasing the likelihood and severity of injuries during crashes. These findings are consistent with prior studies highlighting the role of favorable road conditions in increasing crash severity through behavioral complacency [51].

Lighting effects were statistically significant only in single-vehicle crashes (Table 3). Dark conditions (with and without street lighting) increased the probability of PDO crashes by 5.8% and decreased severe/fatal injuries by 1.6%. This suggests that limited visibility may encourage more cautious driving, particularly in low-traffic, single-vehicle scenarios. The increased PDO risk could be partly due to the limited sight distance availability in dark conditions. However, these effects were not observed in the Multi-Vehicle Model, indicating that lighting-related risk perception is more influential in isolated or less complex crash environments.

4.3. Temporal Patterns

Temporal factors, including year, day of the week, and season, showed meaningful effects on crash severity. In the Multi-Vehicle Model (Table 4), crashes occurring in 2013, 2014, and 2016 exhibited reductions in injury severity. Specifically, crashes in 2013 were associated with a 3.6% increase in PDO crashes and decreases of 2.6% and 1.0% in serious and severe/fatal injuries, respectively. For 2014, PDO crashes increased by 3.0% with corresponding reductions of 2.2% and 0.8% in serious and severe/fatal injuries, and for 2016, PDO crashes increased by 4.9%, with decreases of 3.6% and 1.3% in serious and severe/fatal injuries. These patterns indicate gradual improvements in traffic safety over time.

Day-of-week effects further highlighted temporal trends. Weekday crashes were associated with a 4.1% increase in PDO crashes and decreases of 3.0% and 1.1% in serious and severe/fatal injuries, respectively. These effects likely reflect more structured traffic conditions, predictable travel patterns, lower risk-taking, and a higher proportion of commuter trips. Conversely, weekend travel may contribute to higher crash severity, consistent with prior studies [52,53].

Additionally, seasonal factors also played a role. In single-vehicle crashes (Table 3), winter crashes increased PDO crash probability by 6.1% while reducing serious and severe/fatal injuries by 4.5% and 1.6%, respectively. These effects support the behavioral adaptation hypothesis, which suggests that drivers respond to perceptible hazards by reducing speed, increasing headways, and driving more cautiously [9,46]. Taken together, these findings suggest that temporal trends in crash severity are influenced by a combination of behavioral adaptation, structured traffic patterns, and gradual improvements in road safety management.

4.4. Driving Behaviors

Driving maneuvers and behavioral characteristics of drivers displayed a crucial role in the severity of intersection crashes. The model results showed that certain maneuvers were associated with high injury severity. This was particularly evident for directional crossing movements, such as left turns and passing, which typically involve greater complexity and increased conflict exposure at intersections.

Left turns were found to be among the most influential contributors to increased crash severity. In the Multi-Vehicle Model (Table 4), left turns were associated with a 1.9% increase in severe/fatal injuries, a 4.5% increase in serious injuries, and a 6.4% decrease in PDO crashes. The heightened risk linked to left turns likely stems from prolonged exposure within intersections, increased conflict angles, and the need for precise gap judgment in oncoming traffic. Previous studies similarly identify left turns as among the most hazardous intersection maneuvers, particularly under limited visibility or driver misjudgment [54,55].

In contrast, right-turn maneuvers were associated with reduced crash severity. In the Multi-Vehicle Model, right turns increased PDO crash probability by 18.9%, while reducing serious and severe/fatal injuries by 13.3% and 5.6%, respectively. These results reflect the generally lower speeds, shorter crossing distances, and fewer conflict points associated with right-turn movements, which together reduce the likelihood of high-severity crashes.

Driver age also showed a moderating effect on crash severity. In the Multi-Vehicle Model, each one-unit increase in average driver age was associated with a 0.23% increase in PDO crash probability, along with small decreases of 0.16% and 0.07% in serious and severe/fatal injuries, respectively. Similar effects were observed in single-vehicle crashes. This indicates that older drivers, while potentially facing physical limitations, often adopt more conservative driving behaviors, such as reduced speeds and avoidance of complex maneuvers, thereby mitigating injury severity. This pattern aligns with prior research on risk aversion among older drivers, though it contrasts with studies using categorical age groupings, highlighting the effect of treating age as a continuous variable [56,57].

4.5. Intersection Controls

Intersection control types (signals, signs, stop control) significantly influenced crash severity results. The model results demonstrate that crashes occurring at controlled intersections (those governed by traffic signals or stop signs) tended to be associated with a higher likelihood of injury severity compared to uncontrolled intersections.

In the Multi-Vehicle Model (Table 4), intersections with traffic signals were associated with a 1.7% increase in severe/fatal injuries, a 4.1% increase in serious injuries, and a 5.8% decrease in PDO crashes. Similarly, intersections controlled by stop signs or traffic signs were linked to a 1.4% increase in severe/fatal injuries, a 3.4% increase in serious injuries, and a 4.8% reduction in PDO crashes. These results indicate a consistent relationship between intersection control types and the likelihood of higher-severity outcomes.

Although these findings may appear counterintuitive, they align with prior research suggesting that driver over-reliance on control devices can contribute to more severe crashes when violations or misjudgments occur [58,59,60]. Controlled intersections often carry higher traffic volumes and may create a false sense of predictability, where drivers assume others will obey the rules. When this expectation fails, due to distraction, inattention, or error, collisions tend to occur at higher speeds and sharper angles, increasing the risk of serious or fatal injuries [59].

4.6. Crash Configuration

The type of crash, whether involving a single vehicle or multiple vehicles, strongly shapes injury severity at intersections. Understanding these distinctions is essential because the dynamics, exposure, and risk factors vary substantially between single-vehicle and multi-vehicle collisions. Separate RPOL models for single-vehicle and multi-vehicle crashes reveal these distinct patterns, highlighting how environmental conditions, driver behavior, and roadway design differently influence outcomes depending on crash configuration.

In the Single-Vehicle Model (Table 4), adverse weather and surface conditions were key predictors of crash severity. Winter-season crashes were associated with a 6.1% higher probability of PDO outcomes and reductions in serious (−4.5%) and severe/fatal injuries (−1.6%). Similarly, snowy weather increased PDO likelihood by 12.8% while lowering serious and severe/fatal injury probabilities. These trends suggest that single-vehicle crashes under such conditions often involve reduced speeds or loss of control rather than high-impact collisions. Divided highways also showed a protective effect, likely reflecting safety design features such as medians and shoulders.

Alternatively, the Multi-Vehicle Model (Table 4) highlighted the influence of urban location, turning maneuvers, and intersection control. Urban crashes were associated with a 16.3% increase in PDO likelihood and an 11.6% decrease in serious injuries. Left-turn maneuvers reduced PDO probability by 6.4% and increased severe/fatal outcomes by 1.9%, reflecting higher exposure and conflict angles at intersections. Collector roads and median dividers were linked to lower severity, supporting the value of road design in mitigating crash impact. Driver age exhibited a protective trend in both models. In the Multi-Vehicle Model, each unit increase in average age reduced serious injury risk by 0.16%, suggesting older drivers’ cautious behavior lowers crash severity.

4.7. Comparative Assessment

Incorporating heterogeneity in crash severity models substantially improves their explanatory power. Across all specifications, single-vehicle and multi-vehicle, the RPOL models accounting for heterogeneity in means and variances consistently outperformed fixed-parameter counterparts. For instance, the single-vehicle RPOL model achieved higher log-likelihood, lower AIC and BIC, and a higher Pseudo R² than the model without heterogeneity. Similar improvements were observed in the multi-vehicle models, demonstrating better fit and capturing more nuanced patterns in the data (Table 5).

Moreover, these performance gains reflect the theoretical expectation that driver behavior, roadway interactions, and environmental conditions often exert heterogeneous effects on crash outcomes, which fixed-parameter models cannot adequately capture. The results reinforce the literature advocating for flexible model structures, such as random parameters or mixed logit frameworks, to more accurately reflect the complexity of intersection crash data.

5. Conclusions

This study involves analyzing intersection crash severity using RPOL models with heterogeneity in means and variances based on 9108 crashes recorded in Wyoming, USA, from 2007 to 2017. The models, separately estimated for single-vehicle and multi-vehicle crashes, identified significant influences of roadway characteristics, environmental conditions, temporal patterns, driver behavior, and intersection control on injury severity outcomes. By incorporating random parameters and allowing heterogeneity across observations, the models provided a nuanced understanding of the factors that are influencing crash injury severity risks.

A principal finding indicates that perceptible risk may lead drivers to adopt safer behaviors. Adverse conditions such as snowy weather, wet/icy/snowy road surfaces, and darkness without street lighting were associated with increased probabilities of PDO outcomes and reduced risks of severe injuries or fatalities. This pattern indicates that drivers may exercise greater caution under visible risk. Conversely, the heightened severity on dry roads highlights the potential for behavioral contentment in perceivably safe conditions. Moreover, crashes occurring on collector roads and within urban areas demonstrated reduced risks of serious injuries. This trend likely reflects the influence of design elements such as slower operating speeds, improved infrastructure, and traffic-calming measures.

The analysis also highlighted the influence of driver actions and intersection control types. Left-turn maneuvers were identified as high-risk behaviors significantly increasing the probability of serious and fatal injuries in multi-vehicle crashes due to longer exposure and complex conflict angles. In contrast, right-turn maneuvers exhibited a lower risk profile favoring PDO outcomes. Unexpectedly, intersections with traffic signals and stop signs were associated with higher injury severity compared to uncontrolled locations. This association may partly reflect the higher traffic volumes and complexity of movements typical at controlled intersections rather than the controls themselves. It also suggests that while traffic controls help regulate flow, they may contribute to the occurrences of severe crashes when violations are committed.

Temporal and demographic factors demonstrated moderating influences. Crashes in the later years of the study period and those occurring on weekdays were linked to reduced severity, likely reflecting improvements in vehicle safety, roadway infrastructure, and more predictable traffic patterns. An increase in average driver’s age was also associated with lower severity outcomes consistent with risk-averse driving behavior among older drivers. The ISD variable did not exhibit statistically significant effects, likely due to data limitations stemming from inconsistent or missing records.

To better evaluate ISD-related risks and further refine these findings, future research should incorporate high-resolution intersection data using LiDAR and simulation-based analysis of safety measures. Integrating these advanced data sources can help capture risk precursors that traditional crash databases often overlook. Overall, this study’s modeling framework provides actionable insights for transportation agencies in Wyoming and similar regions. The results can inform practitioners when it comes to targeted safety interventions, intersection design improvements, and behavior-focused policies aimed at mitigating crash severity.